Hopping Conduction in Uniaxially Stressed Si:B near the Insulator-Metal Transition

TL;DR

This study investigates the low-temperature conductivity of p-type Si:B near the insulator-metal transition under uniaxial stress, revealing universal scaling behavior and emphasizing the importance of the prefactor in analyzing critical exponents.

Contribution

It provides a detailed analysis of the universal scaling of conductivity near the transition and clarifies the role of the prefactor, challenging previous assumptions of Mott variable-range hopping.

Findings

Conductivity collapses onto a universal scaling curve.

Prefactor proportional to square root of temperature is crucial for accurate analysis.

Conductivity does not follow Mott variable-range hopping in the critical region.

Abstract

Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor, corresponding to the T-dependence of the critical curve, has been determined reliably for this system, and is proportional to the square-root of T. We show explicitly that nevlecting the prefactor leads to substantial errors in the determination of the scaling parameters and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping in the critical region nor does it obey this form for any range of the parameters. Instead, for smaller argument of the scaling function, the conductivity of Si:B is well fit by an exponential form with exponent 0.31 related to the critical exponents of the system at the metal- insulator transition.